Question:
Prove the following trigonometric identities.
$\tan ^{2} \theta \cos ^{2} \theta=1-\cos ^{2} \theta$
Solution:
We know that, $\sin ^{2} \theta+\cos ^{2} \theta=1$.
So,
$\tan ^{2} \theta \cos ^{2} \theta=(\tan \theta \times \cos \theta)^{2}$
$=\left(\frac{\sin \theta}{\cos \theta} \times \cos \theta\right)^{2}$
$=(\sin \theta)^{2}$
$=\sin ^{2} \theta$
$=1-\cos ^{2} \theta$
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